Ratio Cut, despite normalizing the cut by the size of clusters, intends to separate small clusters, as demonstrated in [1]}, [2]}. For this reason, Normalized Cut has proposed to normalize the cut by the degree of the clusters, rather than the size of the clusters. An alternative way to overcome this problem is to apply a stronger constraint on the size of the clusters. Using this idea, P-Spectral Clustering [3]} proposes a nonlinear generalization of spectral clustering based on the second eigenvector of the graph \(p\) -Laplacian which is then interpreted as a generalization of graph clustering models such as Ratio Cut. P-Spectral Clustering is an iterative clustering procedure that at each step performs a bi-partitioning of one of the existing clusters until \(K\)  clusters are constructed using a nonlinear spectral method.
The underlying respective cost function for bi-partitioning into two sets \(\mathbf {O}_a\)  and \(\mathbf {O}_b\)  is given by (\(p >1\) )
\(R^{PSC}(c,\mathbf {X}) = \sum _{i\in \mathbf {O}_a}\sum _{j\in \mathbf {O}_b} \mathbf {X}_{ij}\left( \frac{1}{|\mathbf {O}_a|^{\frac{1}{p-1}}} + \frac{1}{|\mathbf {O}_b|^{\frac{1}{p-1}}} \right)^{p-1}.\) 
